The present invention relates to a device and method utilizable to calculate the transfer factor and ultimately the geometric shape factor of an object. The geometric shape factor, sometimes called view factor, is an important parameter used in radiative heat transfer analysis. The transfer factor is representative of the radiant energy from a surface i which reaches a surface j, both directly and by reflection from other surfaces. The reflections can be multiple; that is, energy emanating from surface i can reflect off of several surfaces before reaching surface j. The shape factor, or view factor, is the fraction of energy emitted by a surface i which is intercepted directly by surface j. The shape factor is highly dependent on the relative distance separating surfaces i and j and their angular orientation with respect to each other.
The calculation of theoretical shape factors is an important step in the design process. Shape factors are necessary to the fundamental heat transfer equations which describe the radiative heat transfer characteristics of any system. It is economically necessary to know the radiative heat transfer characteristics during the design process, and before construction. In the event that a particular design offering other advantages would produce too severe a temperature profile, it can be altered to eliminate the harmful profile without the excessive costs of reconstruction. The geometry of an array of objects receiving radiation, reflecting radiation or emitting radiation, can cause high temperature gradients over small areas which may degrade its structural integrity. It is therefore necessary to ascertain the radiative heat into and out of relatively small areas of the structure. Procurement of the shape factors is an expensive and integral part of the radiative heat transfer analysis.
Calculating a shape factor for two surfaces of simple geometric shape is relatively easy since the known geometric characteristics of the surfaces and the known distances and orientations of the surfaces simplify the problem. The total radiative flux into or out of a surface is dependent upon radiation exposure, temperature, orientation and reflectivity of each surface. Radiative flux leaving surface i, in the presence of a surface j, equals its temperature to the fourth power times its emissivity and times the Stefan Boltzman constant, as well as that portion of the radiative flux received from surface j which is reflected from surface i. Radiative flux entering surface i equals that portion of the radiative flux received from surface j which is not reflected but absorbed.
The radiative flux received at surface i from surface j, and the radiative flux received at surface j from surface i is highly dependent upon the areas of the surfaces and their distance and geometric orientation. This complex geometric data is, for any two surfaces, reducible to a single ratio of the percent of radiative energy at one surface received at the other surface. This percent of radiative energy transfer is the geometric shape factor.
It is evident that adding additional surfaces increases both the number of surfaces for which emissive radiation calculations must be performed as well as increasing the reflectivity components for all surfaces, for each additional surface. Thus the flux to be calculated for each surface increases as N+ (N-1)N or N.sup.2 for additional surfaces. For a complex object, it is desirable to "divide" the surface of an object into as many small surfaces or "nodes" as possible in order to get a more exact temperature profile. But when the number of nodes are increased, the calculational steps increase profusely. Another complication when many surfaces are involved is "shadowing," the blockage of the view of surface j from surface i by a surface k.
A good example of a case wherein the calculation of shape factor is critical is in the design of an orbiting space station. The extremes of heat and cold, as well as the need to expel generated energy, make heat transfer calculations and the shape factor calculations critical to the design process. The great expense involved in construction prohibits the construction of a full scale model for thermal testing. Even if such a model were constructed, the conditions to which the structure would be subjected in the space environment would be almost impossible to simulate on earth.
Conventional shape factor and thermal analysis calculation methods are relatively time consuming, especially if high accuracy is required. Computers programmed to characterize the thermal environments of a space structure using current methods would be expected to consume over 5,000 hours of computing time. Of this figure, about 4,000 hours would be needed to calculate the shape factors. At the present cost of computer time, such thermal characterization is estimated to exceed five million dollars.
It is well known in the aerospace industry that numerous designs necessary to a single project will require numerous design modifications throughout the design phase of the project. The prohibitive cost of calculating even a single set of shape factors for a single design becomes even more acutely cost Prohibitive when recalculation necessitated by design modification is required. With existing methods, a change in the configuration of the object requires a complete recalculation of the shape factors. At the current high cost of calculation, design modifications would be extremely costly.
Given the extensive computer time required for analysis, interactive computer design is also extremely costly, if not impossible, using current design methods. A design modification intended to remedy a problem in one part of the system could produce a deleterious effect elsewhere which would be discoverable only by a complete analysis of the shape factors.
Another problem encountered involves the nonidealities of the surface being measured. The ideal surface is one which emits and reflects radiation away from the surface with an intensity directed in all directions equally. A surface possessing this characteristic is termed a Lambertian surface. A non-ideal surface has a tendency to forward scatter and backscatter radiation to a greater extent than a Lambertian surface.
In a conventional system of calculation, the non-ideality of a surface is not able to be taken to account in the calculations without further coding for more complex calculations. Such calculations would require a table of bidirectional reflectivity factors for each type of surface material used and use of the Monte Carlo computional algorithm which is known to be extremely costly.